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Using the mixed space representation, we extend our earlier analysis to thecase of Dirac and gauge fields and show that in the absence of a chemicalpotential, the finite temperature Feynman diagrams can be related to thecorresponding zero temperature graphs through a thermal operator. At non-zerochemical potential we show explicitly in the case of the fermion self-energythat such a factorization is violated because of the presence of a singularcontact term. Such a temperature dependent term which arises only at finitedensity and has a quadratic mass singularity cannot be related, through aregular thermal operator, to the fermion self-energy at zero temperature whichis infrared finite. Furthermore, we show that the thermal radiative correctionsat finite density have a screening effect for the chemical potential leading toa finite renormalization of the potential.Comment: 13 pages, 4 figures. Revised version (minor changes) accepted for  publication in Phys. Rev.

Thermal operator representation of finite temperature graphs. II.